One-dimensional Riemannian foliations on the Heisenberg group.

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dc.contributor.advisorWalschap, Gerard,en_US
dc.contributor.authorMunteanu, Marius Ionut.en_US
dc.date.accessioned2013-08-16T12:18:48Z
dc.date.available2013-08-16T12:18:48Z
dc.date.issued2002en_US
dc.description.abstractThe main goal of our dissertation is to show that one-dimensional Riemannian foliations on the Heisenberg group H2 n+1 are homogeneous. Using our result and the homogeneity of codimension one Riemannian foliations on H 2n+1 proved by G. Walschap, we conclude that every Riemannian foliation on the three-dimensional Heisenberg group is homogeneous.en_US
dc.description.abstractAs noted in the literature, the result mentioned above remains valid on Gamma\H3, where Gamma is a lattice in H3. We give another proof for this theorem and we improve it by showing that there are no codimension one foliations on Gamma\H2n +1. We also show that the only one-dimensional Riemannian foliation on the space above occurs as the projection of the foliation on H 2n+1 with leaves tangent to the center.en_US
dc.format.extentv, 48 leaves ;en_US
dc.identifier.urihttp://hdl.handle.net/11244/528
dc.noteAdviser: Gerard Walschap.en_US
dc.noteSource: Dissertation Abstracts International, Volume: 63-11, Section: B, page: 5283.en_US
dc.subjectGeodesics (Mathematics)en_US
dc.subjectLie algebras.en_US
dc.subjectMathematics.en_US
dc.subjectGeometry, Riemannian.en_US
dc.subjectVector spaces.en_US
dc.subjectGeometry, Differential.en_US
dc.thesis.degreePh.D.en_US
dc.thesis.degreeDisciplineDepartment of Mathematicsen_US
dc.titleOne-dimensional Riemannian foliations on the Heisenberg group.en_US
dc.typeThesisen_US
ou.groupCollege of Arts and Sciences::Department of Mathematics
ou.identifier(UMI)AAI3070633en_US

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